# What is the formula for resonance in a series and parallel circuit?

I thought there was only one forumla but apparently there are two? any ideas what they are?

### 3 Answers

- BonyLv 510 years agoBest answer
** In practice, the same formula, as you say is used for

both series and parallel resonance LC circuits.

However when such circuits contain significant resistance,

there is a resonant formula which includes this R as well

as the L and C, for parallel circuits only.. The result of using

the LCR formula compared to the LC formula, produces a

frequency difference which would be exceeded by the

variation due to the tolerance of the L and C components.

For that practical reason the LCR formula is seldom used.

The R is considered as being in series with L, with C in

parallel with the LR series combination.

Bandwidth, Q, Impedence, and Power Losses

are other factors of concern in such circuits.

See both formula and circuits, re the above at my LINK.

- vadaptreLv 510 years ago
reactance of capacitor=1/(2*pi*f*C)..reactance of inductor=2*pi*f*L

when these two components are in series, the net impedance is zero, so current flow from source is effectively infinite..ie resonance..this occurs when Xc=Xl..>f=1/(2*pi*rt(L*C)

in a parallel LC circuit the effective impedance is infinite for the same relationship and resonance is where the current oscill8s with no input from the source

As for the effect of real ohmic resistance, analysis shows..

parallel circuit..R series L.>f increases..R series C >f decreases

series circuit R parallel L ..>f increases..R parallel with C> f decreases

obv for parallel circuit parallel R has no effect on res freq..as neither does series R in series resonant circuit (except on the 'sharpness' of the peak min/max @ resonance!)

u cud go mad analysing 2nd order effects due to capacitors having parasitic inductance and resistance and inductors with parasitic capacitance, resistance..but life's 2 short!

Source(s): madeitup!